Five-axis milling is an advanced manufacturing technology commonly used for creating complex geometries in the automobile, aerospace, mold-making, and energy industries. It offers higher shaping capability and productivity than traditional three-axis machining does, with two rotational degrees of freedom in the tool motion. Five-axis milling operations are classified into end milling and flank milling according to how the cutter removes stock material. In flank milling, the cutting edges along the cutter peripheral, generally of a cylindrical or conical shape, perform the cutting action. Tool path planning in five-axis flank milling remains challenging. Completely eliminating tool overcut and undercut is highly difficult, if not impossible. In practice, the finished surface is considered acceptable when the amount of geometrical deviations is within a given tolerance. However, effective methods of controlling the deviations are still lacking in five-axis flank machining.
For reducing the geometrical deviations (not considering the errors induced physically such as cutter deflection and tool wear) produced in five-axis flank milling, past studies have proposed numerous tool path planning methods based on optimization schemes. Various optimization methods have been proposed for adjusting cutter locations simultaneously by applying an objective function to minimize the accumulated geometrical deviations of the finished surface. These methods demonstrate the following drawbacks. The computational efficiency is low in a high-dimensional search space corresponding to a large number of cutter locations. In addition, both the tool center point and axis must be modified during the optimization process. Such modifications are particularly observable at the cutter locations around the surface regions of excessive twist. Uneven modifications of the tool motion often result in poor surface roughness on the finished part.